An Approximation Algorithm for Shortest Descending Paths

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No ecient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We give a simple approximation algorithm that solves the SDP problem on general terrains. Our algorithm discretizes the terrain with O(n 2 X/†) Steiner points so that after an O ‡ n 2 X † log i nX

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